Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to
cryptography
factoring
primality testing
complexity analysis
computer arithmetic
computational number theory
Fundamental Number Theory with Applications also covers:
Carmichael numbers
Dirichlet products
Jacobsthal sums
Mersenne primes
perfect numbers
powerful numbers
self-contained numbers
Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material.
Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 235 mm
Breite: 156 mm
Gewicht
ISBN-13
978-0-8493-3987-5 (9780849339875)
Schweitzer Klassifikation
Arithmetic of the Integers
Introduction - Where We Begin and Why
The Fundamental Laws
Divisibility
Prime Numbers
Computer Arithmetic and Complexity
Applications to a Set of Quadratics
Congruences
The Basics
Linear Congruences
Arithmetic Functions - Euler's Totient
The Chinese Remainder Theorem
Polynomial Congruences and Thue's Theorem
Cryptography and Factoring
Quadratic Polynomials
Primitive Roots
Order
Existence
Indices
Primality Testing and Cryptography
Quadratic Orders, Ideals and Units
Quadratic Residues
The Quadratic Reciprocity Law
The Jacobi and Kronecker Symbols
Quadratic Polynomials and Primes
Quadratic Residues and Primality Testing
Applications to Quadratic Orders
Continued Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Continued Fractions and Factoring
The Continued Fraction Algorithm
Diophantine Equations
Sums of Squares
The Equation x2 - Dy2 = n
Diophantine Equations of Higher Degree
Elliptic Curves, Factoring, and Primality
Applications: Algebraic Number Theory
Appendices
A. Set Theory
B. Primes = 9547 and Least Primitive Roots
C. Tables of Special Primes
D. Cunningham Factorizations
E. Pseudoprimes and Carmichael Numbers
F. Indices
G. Values of Some Arithmetic Functions
H. The ABC Conjecture
I. The Prime Number Theorem
Solutions to Odd-Numbered Exercises
Bibliography
List of Symbols
Index
